Decorrelation-Based Feature Discovery: Saliva-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

1.2 Data: The COVID_19 Data-Set

The data to process is described in:

https://zenodo.org/record/4156647#.Y1bSF3bMKUk

IR Saliva Testing Dataset

10.5281/zenodo.4156647 https://doi.org/10.5281/zenodo.4156647

I added a column to the data identifying the repeated experiments.

SalivaIR <- as.data.frame(read_excel("~/GitHub/FCA/Data/SalivaThermal_Source_Data_2.xlsx"))


SalivaIR_set1 <- subset(SalivaIR,RepID==1)
rownames(SalivaIR_set1) <- SalivaIR_set1$ID
SalivaIR_set1$RepID <- NULL
SalivaIR_set1$ID <- NULL
SalivaIR_set1$Ct <- NULL

SalivaIR_set2 <- subset(SalivaIR,RepID==2)
rownames(SalivaIR_set2) <- SalivaIR_set2$ID
SalivaIR_set2$RepID <- NULL
SalivaIR_set2$ID <- NULL
SalivaIR_set2$Ct <- NULL

SalivaIR_set3 <- subset(SalivaIR,RepID==3)
rownames(SalivaIR_set3) <- SalivaIR_set3$ID
SalivaIR_set3$RepID <- NULL
SalivaIR_set3$ID <- NULL
SalivaIR_set3$Ct <- NULL

SalivaIR_Avg <- (SalivaIR_set1 + SalivaIR_set2 + SalivaIR_set3)/3


colnames(SalivaIR_Avg) <- paste("V",colnames(SalivaIR_Avg),sep="_")

SalivaIR_Avg$class <- 1*(str_detect(rownames(SalivaIR_Avg),"P"))

pander::pander(table(SalivaIR_Avg$class))

0	1
30	31

1.2.0.1 Standarize the names for the reporting

studyName <- "IRSaliva"
dataframe <- SalivaIR_Avg
outcome <- "class"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
61	251

pander::pander(table(dataframe[,outcome]))

0	1
30	31

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.999994

1.5 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  Included: 224 , Uni p: 0.001116071 , Outcome-Driven Size: 0 , Base Size: 1 , Rcrit: 0.384269 
#> 
#> 
 1 <R=1.000,thr=0.900,N=  224>, Top: 1( 223 )[ 1 : 1 Fa= 1 : 0.900 ]( 1 , 223 , 0 ),<|>Tot Used: 224 , Added: 223 , Zero Std: 0 , Max Cor: 1.000
#> 
 2 <R=1.000,thr=0.900,N=  224>, Top: 5( 71 )[ 1 : 5 Fa= 6 : 0.900 ]( 5 , 158 , 1 ),<|>Tot Used: 224 , Added: 158 , Zero Std: 0 , Max Cor: 1.000
#> 
 3 <R=1.000,thr=0.900,N=  224>, Top: 11( 4 )[ 1 : 11 Fa= 17 : 0.900 ]( 11 , 149 , 6 ),<|>Tot Used: 224 , Added: 149 , Zero Std: 0 , Max Cor: 0.999
#> 
 4 <R=0.999,thr=0.900,N=  224>, Top: 21( 5 )=[ 2 : 21 Fa= 35 : 0.928 ]( 21 , 151 , 17 ),<|>Tot Used: 224 , Added: 151 , Zero Std: 0 , Max Cor: 1.000
#> 
 5 <R=1.000,thr=0.900,N=  224>, Top: 36( 4 )[ 1 : 36 Fa= 71 : 0.900 ]( 36 , 134 , 35 ),<|>Tot Used: 224 , Added: 134 , Zero Std: 0 , Max Cor: 0.997
#> 
 6 <R=0.997,thr=0.900,N=  224>, Top: 39( 4 )[ 1 : 39 Fa= 109 : 0.900 ]( 39 , 83 , 71 ),<|>Tot Used: 224 , Added: 83 , Zero Std: 0 , Max Cor: 0.995
#> 
 7 <R=0.995,thr=0.900,N=  224>, Top: 25( 2 )[ 1 : 25 Fa= 134 : 0.900 ]( 25 , 32 , 109 ),<|>Tot Used: 224 , Added: 32 , Zero Std: 0 , Max Cor: 0.985
#> 
 8 <R=0.985,thr=0.900,N=  224>, Top: 4( 1 )[ 1 : 4 Fa= 138 : 0.900 ]( 4 , 4 , 134 ),<|>Tot Used: 224 , Added: 4 , Zero Std: 0 , Max Cor: 0.899
#> 
 9 <R=0.899,thr=0.800,N=   77>, Top: 34( 1 )[ 1 : 34 Fa= 143 : 0.800 ]( 34 , 41 , 138 ),<|>Tot Used: 224 , Added: 41 , Zero Std: 0 , Max Cor: 0.993
#> 
 10 <R=0.993,thr=0.900,N=   20>, Top: 10( 1 )[ 1 : 10 Fa= 143 : 0.900 ]( 10 , 10 , 143 ),<|>Tot Used: 224 , Added: 10 , Zero Std: 0 , Max Cor: 0.995
#> 
 11 <R=0.995,thr=0.900,N=   20>, Top: 4( 1 )[ 1 : 4 Fa= 145 : 0.900 ]( 4 , 4 , 143 ),<|>Tot Used: 224 , Added: 4 , Zero Std: 0 , Max Cor: 0.950
#> 
 12 <R=0.950,thr=0.900,N=   20>, Top: 1( 1 )[ 1 : 1 Fa= 146 : 0.900 ]( 1 , 1 , 145 ),<|>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.893
#> 
 13 <R=0.893,thr=0.800,N=   26>, Top: 12( 1 )[ 1 : 12 Fa= 149 : 0.800 ]( 12 , 14 , 146 ),<|>Tot Used: 224 , Added: 14 , Zero Std: 0 , Max Cor: 0.977
#> 
 14 <R=0.977,thr=0.900,N=    8>, Top: 4( 1 )[ 1 : 4 Fa= 151 : 0.900 ]( 4 , 4 , 149 ),<|>Tot Used: 224 , Added: 4 , Zero Std: 0 , Max Cor: 0.862
#> 
 15 <R=0.862,thr=0.800,N=   10>, Top: 5( 1 )[ 1 : 5 Fa= 151 : 0.800 ]( 5 , 5 , 151 ),<|>Tot Used: 224 , Added: 5 , Zero Std: 0 , Max Cor: 0.944
#> 
 16 <R=0.944,thr=0.900,N=    2>, Top: 1( 1 )[ 1 : 1 Fa= 151 : 0.900 ]( 1 , 1 , 151 ),<|>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.842
#> 
 17 <R=0.842,thr=0.800,N=    4>, Top: 2( 1 )[ 1 : 2 Fa= 151 : 0.800 ]( 2 , 2 , 151 ),<|>Tot Used: 224 , Added: 2 , Zero Std: 0 , Max Cor: 0.994
#> 
 18 <R=0.994,thr=0.900,N=    2>, Top: 1( 1 )[ 1 : 1 Fa= 152 : 0.900 ]( 1 , 1 , 151 ),<|>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.891
#> 
 19 <R=0.891,thr=0.800,N=    2>, Top: 1( 1 )[ 1 : 1 Fa= 152 : 0.800 ]( 1 , 1 , 152 ),<|>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.896
#> 
 20 <R=0.896,thr=0.800,N=    2>, Top: 1( 1 )[ 1 : 1 Fa= 152 : 0.800 ]( 1 , 1 , 152 ),<|>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.799
#> 
 21 <R=0.799,thr=0.800,N=    2>
#> 
 [ 21 ], 0.7994991 Decor Dimension: 224 Nused: 224 . Cor to Base: 223 , ABase: 1 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

5.5

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

0.0357

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

5.08

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

0.969

1.5.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPLTM <- attr(DEdataframe,"UPLTM")
  
  gplots::heatmap.2(1.0*(abs(UPLTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
}

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after IDeA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.7994991

1.8 U-MAP Visualization of features

1.8.1 The UMAP based on LASSO on Raw Data

if (nrow(dataframe) < 1000)
{
  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  datasetframe.umap = umap(scale(dataframe[1:numsub,varlist]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
}

1.8.2 The decorralted UMAP

if (nrow(dataframe) < 1000)
{

  datasetframe.umap = umap(scale(DEdataframe[1:numsub,varlistc]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
}

1.9 Univariate Analysis

1.9.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : V_1064 200 : V_854

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_V_1064 200 : La_V_854

1.9.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
V_908	0.221	0.128	0.261	0.117	0.579	0.596
V_906	0.220	0.127	0.261	0.117	0.585	0.596
V_904	0.220	0.127	0.261	0.117	0.592	0.596
V_892	0.219	0.127	0.261	0.121	0.626	0.596
V_890	0.219	0.127	0.261	0.121	0.616	0.596
V_888	0.219	0.127	0.261	0.122	0.603	0.596
V_912	0.223	0.129	0.263	0.117	0.604	0.595
V_910	0.222	0.128	0.262	0.117	0.587	0.595
V_896	0.220	0.127	0.261	0.120	0.620	0.595
V_894	0.219	0.127	0.261	0.121	0.625	0.595

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
La_V_1054	-3.44e-03	1.80e-02	-2.04e-02	1.20e-02	0.9818	0.795
La_V_934	7.79e-05	1.13e-04	1.94e-04	2.51e-04	0.2394	0.771
La_V_1004	2.04e-04	2.47e-03	2.02e-03	1.55e-03	0.2181	0.766
La_V_916	1.52e-03	3.29e-03	3.71e-03	4.33e-03	0.0363	0.763
La_V_848	7.39e-04	2.64e-03	-5.58e-04	1.13e-03	0.3681	0.760
La_V_1266	-2.22e-03	3.07e-03	-5.09e-03	3.63e-03	0.1002	0.754
La_V_1128	3.06e-04	9.96e-04	-3.28e-04	6.81e-04	0.0627	0.743
La_V_1018	2.65e-05	9.57e-05	6.95e-05	5.35e-05	0.6595	0.743
La_V_810	1.42e-05	3.63e-05	3.79e-05	2.28e-05	0.7256	0.735
La_V_1102	-9.87e-04	7.12e-03	5.03e-03	5.69e-03	0.4870	0.734

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
5.65	223	0.996

theCharformulas <- attr(dc,"LatentCharFormulas")


finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores
La_V_1054	- (1.017)V_1138 + V_1054 - (3.036)V_986 + (3.026)V_974	-3.44e-03	1.80e-02	-2.04e-02	1.20e-02	0.9818	0.795	0.547	21
La_V_934	- (5.73e-04)V_1138 + V_934 - (1.847)V_932 + (0.847)V_930 + (1.19e-03)V_872	7.79e-05	1.13e-04	1.94e-04	2.51e-04	0.2394	0.771	0.584	-1
La_V_1004	+ (0.016)V_1138 - (1.011)V_1006 + V_1004	2.04e-04	2.47e-03	2.02e-03	1.55e-03	0.2181	0.766	0.571	2
La_V_916	+ (0.041)V_1138 - (0.956)V_930 + V_916 - (0.074)V_872	1.52e-03	3.29e-03	3.71e-03	4.33e-03	0.0363	0.763	0.594	10
La_V_848	- (5.65e-03)V_1138 + (0.638)V_872 - (1.615)V_860 + V_848	7.39e-04	2.64e-03	-5.58e-04	1.13e-03	0.3681	0.760	0.589	-3
La_V_1266	- (0.933)V_1282 + V_1266 - (0.077)V_1222 - (7.72e-03)V_1138	-2.22e-03	3.07e-03	-5.09e-03	3.63e-03	0.1002	0.754	0.544	2
La_V_1128	+ (0.601)V_1138 - (1.601)V_1132 + V_1128	3.06e-04	9.96e-04	-3.28e-04	6.81e-04	0.0627	0.743	0.560	3
La_V_1018	+ (1.95e-04)V_1138 - (0.964)V_1024 + (2.886)V_1022 - (2.920)V_1020 + V_1018 - (2.29e-03)V_872	2.65e-05	9.57e-05	6.95e-05	5.35e-05	0.6595	0.743	0.557	-5
La_V_810	+ (1.20e-04)V_1138 + V_810 - (2.673)V_808 + (2.006)V_806 - (0.333)V_802	1.42e-05	3.63e-05	3.79e-05	2.28e-05	0.7256	0.735	0.569	-4
La_V_1102	- (0.278)V_1138 + V_1102 - (0.715)V_1086	-9.87e-04	7.12e-03	5.03e-03	5.69e-03	0.4870	0.734	0.560	9
V_908	NA	2.21e-01	1.28e-01	2.61e-01	1.17e-01	0.5785	0.596	0.596	NA
V_906	NA	2.20e-01	1.27e-01	2.61e-01	1.17e-01	0.5848	0.596	0.596	NA
V_904	NA	2.20e-01	1.27e-01	2.61e-01	1.17e-01	0.5918	0.596	0.596	NA
V_892	NA	2.19e-01	1.27e-01	2.61e-01	1.21e-01	0.6256	0.596	0.596	NA
V_890	NA	2.19e-01	1.27e-01	2.61e-01	1.21e-01	0.6163	0.596	0.596	NA
V_888	NA	2.19e-01	1.27e-01	2.61e-01	1.22e-01	0.6032	0.596	0.596	NA
V_912	NA	2.23e-01	1.29e-01	2.63e-01	1.17e-01	0.6041	0.595	0.595	NA
V_910	NA	2.22e-01	1.28e-01	2.62e-01	1.17e-01	0.5866	0.595	0.595	NA
V_896	NA	2.20e-01	1.27e-01	2.61e-01	1.20e-01	0.6202	0.595	0.595	NA
V_894	NA	2.19e-01	1.27e-01	2.61e-01	1.21e-01	0.6248	0.595	0.595	NA

1.10 Comparing IDeA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA

EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }

pander::pander(table(dataframe[,outcome],pr))

	0	1
0	30	0
1	17	14

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.721	0.592	0.829
3	se	0.452	0.273	0.640
4	sp	1.000	0.884	1.000
6	diag.or	Inf	NA	Inf

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="IDeA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	25	5
1	2	29

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.885	0.778	0.953
3	se	0.935	0.786	0.992
4	sp	0.833	0.653	0.944
6	diag.or	72.500	12.919	406.851

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	23	7
1	3	28

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.836	0.719	0.918
3	se	0.903	0.742	0.980
4	sp	0.767	0.577	0.901
6	diag.or	30.667	7.117	132.134

par(op)

1.11.1 EFA

  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }

  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	29	1
1	16	15

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.721	0.592	0.829
3	se	0.484	0.302	0.669
4	sp	0.967	0.828	0.999
6	diag.or	27.188	3.282	225.207

  par(op)